Rheological modeling with Hookean bead-spring cubes

In this study a general bead-spring model is used for predicting some rheological properties of a cubic bead-spring structure of arbitrary size immersed in a Newtonian solvent. The topology of this bead-spring structure is based upon the well-known cubic crystals (SC, BCC or FCC) and it consists of equal Hookean springs and beads with equal friction coefficients, while hydrodynamic interaction is not included. An appropriate combination of the equations of motion, the expression for the stress tensor and the equation of continuity leads to an explicit constitutive equation with three sets of relaxation times belonging to the three types of bead-spring cubes (SC, BCC or FCC). For small-amplitude oscillatory shear flow it is found that the three relaxation spectra, which are significantly different, result in dynamic moduli which differ mainly in one aspect: the characteristic SC, BCC and FCC time scales are different. The BCC and FCC time scales can be obtained by multiplication of the SC time scale by the ratios M sc/M bcc and M sc/M fcc respectively, where M sc, M bcc and M fcc denote the number of springs in the three types of cubic bead-spring structures.